Personal Profile of Prof. Ruth Charney

Ruth Charney is Professor of Mathematics at Brandeis University. She received her PhD from Princeton University in 1977 and held a postdoctoral position at UC Berkeley, followed by an NSF Postdoctoral Fellowship and assistant professor position at Yale. She spent 18 years as a member of the Ohio State University Mathematics Department before returning to Brandeis University, her undergraduate alma mater, in 2003. In addition, she has held visiting positions at the IAS in Princeton, the IHES in Paris, the Oxford University Mathematical Institute, and the ETH in Zurich.

Ruth is interested in the interplay between topology and algebra. Her research spans several areas of mathematics, including K-theory, algebraic topology, and her current area of interest, geometric group theory. She was recently named a Fellow of the American Mathematical Society.

Ruth is involved in a variety of professional activities. She has served as a Vice President of the American Mathematical Society (AMS) and is currently on the AMS Board of Trustees. She has also served as a member of the U.S. National Committee for Mathematics, and as an editor of the journal Algebraic and Geometric Topology.

Many of her professional activities are aimed at encouraging and mentoring women in mathematics. She is currently President of the Association for Women in Mathematics.

The Morse boundary of a geodesic metric space is a topological space consisting of equivalence classes of geodesic rays satisfying a Morse condition. A key property of this boundary is quasi-isometry invariance: a quasi-isometry between two proper geodesic metric spaces induces a homeomorphism on their Morse boundaries. In the case of a hyperbolic metric space, the Morse boundary is the usual Gromov boundary and Paulin proved that this boundary, together with its quasi-mobius structure, determines the space up to quasi-isometry. I will discuss an analogue of Paulin’s theorem for Morse boundaries of CAT(0) spaces. This is joint work with Devin Murray.

The talk will begin with a brief history of CAT(0) geometry, including some long-standing open problems. Then I will discuss more recent developments and areas of current interest, including the theory of CAT(0) cube complexes and the interplay between CAT(0) geometry and hyperbolic geometry